The functorial structure of type constructors is the foundation for manydefinition and proof principles in higher-order logic (HOL) In this article, we tackle the preservation question forquotients, the last principle for introducing new types in HOL . Surprisingly, lifting the structure in theobvious manner fails for some quotients . We provide astrictly more general lifting scheme that supports such problematic quotients. We extend the Isabelle/HOL proof assistant with a command that automates theregistration of a quotient type as a BNF, reducing the proof burden on the user from the full set of BNF axioms to our inheritance conditions. We demonstratethe command’s usefulness through several case studies. We demonstrate the command’s usefulness through a number of case studies .

Author(s) : Basil Fürer, Andreas Lochbihler, Joshua Schneider, Dmitriy Traytel

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Keywords : hol - command - proof - quotients - studies -

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